9.f4 looks just wrong after either 9...cd4 or 9...Nc6.

7.Qh5 is not the best reaction, imho. Better is 7.Bxe7 which is a regular Classical French, but both sides have inserted h4 and h6, which is to white's advantage (after 7...Qxe7 8.f4).

I may be wrong, but I think that after 7.Bxe7 Qxe7 8.f4 the insertion of the moves h4 and ...h6, compared to the regular main variation, slightly favors white.

I am sure that accepting the gambit gives White a great game. The reason I do not like 6.h4 that much is that Black may ignore it completely, and play a developing move- best seems 6...Nc6! when I am not sure if white has any advantage at all (in that case the h2-h4 move is quite commital). Morozevich and Ni Hua have played 6...Nc6 with great results (probably because they are super strong players, and not because this move is that strong). I prefer the classical 6.Bxe7 Qxe7 7.f4, when white has the usual slight positional advantage (some space, and black has to act smartly to avoid ending up to a bad bishop endgame).